Hox genes are known from a wide variety of organisms. In arthropods, these genes control segment characteristics. Trilobites, being arthropods, probably contained eight major Hox genes that controlled their segment types. The trilobite Bauplan contains eight regions that are most likely under the influence of one or more of these Hox genes. The cephalon contains the frontal lobe, glabellar, and occipital ring regions; the thorax contains the anterior thoracic and posterior thoracic regions; and the pygidium contains the articulating ring, axial, and terminal piece regions. Changes in character distribution within or between these regions represent homeotic evolution, which may have resulted from the modification of Hox transcription or of downstream regulatory genes. A phylogenetic analysis is used to recognize homeotic evolution in trilobites, leading to the conclusion that homeotic evolution is common among Cambrian trilobites.

Temporal asymmetries in clade histories have often been studied in lower Paleozoic radiations. Post-Paleozoic patterns, however, are less well understood. In this paper, disparity and diversity changes in Mesozoic heart urchins were analyzed at the ordinal level, with contrasts among the sister groups Holasteroida and Spatangoida, their paraphyletic stem group Disasteroida the more inclusive clade, the superorder Atelostomata. A 38-dimensional landmark-based morphospace representing test architecture was used to describe morphological evolution in terms of total variance and total range. Discordances between disparity and diversity were evident and were expressed both as deceleration in morphological diversification in all groups and as disproportionately higher disparity early in the histories of the Atelostomata, Holasteroida Spatangoida. The finding that the early atelostomate disparity peak coincides with the origin of the orders Holasteroida and Spatangoida lends support to the perception of orders as semi-independent entities in the biological hierarchy and as meaningful proxies for morphological distinctness.

A comparison of holasteroid and spatangoid responses to the end-Cretaceous mass extinction revealed morphological selectivity. Paleocene spatangoid survivors showed no change in disparity relative to the Campanian-Maastrichtian sample, suggesting nonselectivity. Holasteroids suffered a pronounced loss in disparity (despite a rather high Late Cretaceous level of disparity), indicating morphological selectivity of extinction.

Partitioning of disparity into plastral and nonplastral components, reflecting different degrees of developmental entrenchment and functionality, suggests that the origin of holasteroids and spatangoids is more consistent with an exploration of the developmental flexibility of nonplastral constructions than with uniform ecospace occupation. Within groups, several patterns were also most consistent with intrinsic controls. For plastral landmarks, there is an apparent increase in developmental modularity and decrease in developmental constraint from disasteroids to holasteroids and spatangoids. For nonplastral landmarks, no substantial change in disparity was observed from disasteroids to holasteroids and spatangoids, suggesting the maintenance of a developmental constraint despite the passage of time and ecological differentiation. More generally, this study suggests that certain topologies of disparity and evolutionary mechanisms potentially characteristic of the lower Paleozoic radiations of higher taxa (e.g., developmental flexibility) need not be confined to any given time period or hierarchical level.

Following the end-Ordovician extinction, global clade diversity of Silurian trilobites dropped to about half of Ordovician levels. Although clade diversity failed to recover, this extinction had surprisingly little long-term impact on the number of trilobite species that occupied local habitats (alpha diversity). A new compilation of data from Laurentia and other continents indicates that Silurian trilobite alpha diversities in all major environments were comparable to those of the Late Cambrian and Ordovician; shallow subtidal diversity reached an all-time high during the Late Ordovician. The profound differences in patterns at local and global levels demonstrate the necessity for a hierarchical approach to analyses of diversity. Factors governing global clade diversity are lodged at hierarchical levels beyond those controlling local species richness and must be sought in studies of between-habitat (beta) or geographic (gamma) diversity.

Mathematical modeling of cladogenesis and fossil preservation is used to explore the expected behavior of commonly used measures of taxonomic diversity and taxonomic rates with respect to interval length, quality of preservation, position of interval in a stratigraphic succession, and taxonomic rates themselves. Particular attention is focused on the independent estimation of origination and extinction rates. Modeling supports intuitive and empirical arguments that single-interval taxa, being especially sensitive to variation in preservation and interval length, produce many undesirable distortions of the fossil record. It may generally be preferable to base diversity and rate measures on estimated numbers of taxa extant at single points in time rather than to adjust conventional interval-based measures by discarding single-interval taxa.

A combination of modeling and empirical analysis of fossil genera supports two major trends in marine animal evolution. (1) The Phanerozoic decline in taxonomic rates is unlikely to be an artifact of secular improvement in the quality of the fossil record, a point that has been argued before on different grounds. (2) The post-Paleozoic rise in diversity may be exaggerated by the essentially complete knowledge of the living fauna, but this bias is not the principal cause of the pattern. The pattern may partly reflect a secular increase in preservation nevertheless.

Apparent temporal variation in taxonomic rates can be produced artificially by variation in preservation rate. Some empirical arguments suggest, however, that much of the short-term variation in taxonomic rates observed in the fossil record is real. (1) For marine animals as a whole, the quality of the fossil record of a higher taxon is not a good predictor of its apparent variability in taxonomic rates. (2) For a sample data set covering a cross-section of higher taxa in the Ordovician, most of the apparent variation in origination and extinction rates is not statistically attributable to independently measured variation in preservation rates. (3) Previous work has shown that standardized sampling to remove effects of variable preservation and sampling yields abundant temporal variation in estimated taxonomic rates. While modeling suggests which rate measures are likely to be most accurate in principle, the question of how best to capture true variation in taxonomic rates remains open.

Multicellular filaments from the ca. 1200-Ma Hunting Formation (Somerset Island, arctic Canada) are identified as bangiacean red algae on the basis of diagnostic cell-division patterns. As the oldest taxonomically resolved eukaryote on record Bangiomorpha pubescens n. gen. n. sp. provides a key datum point for constraining protistan phylogeny. Combined with an increasingly resolved record of other Proterozoic eukaryotes, these fossils mark the onset of a major protistan radiation near the Mesoproterozoic/Neoproterozoic boundary.

Differential spore/gamete formation shows Bangiomorpha pubescens to have been sexually reproducing, the oldest reported occurrence in the fossil record. Sex was critical for the subsequent success of eukaryotes, not so much for the advantages of genetic recombination, but because it allowed for complex multicellularity. The selective advantages of complex multicellularity are considered sufficient for it to have arisen immediately following the appearance of sexual reproduction. As such, the most reliable proxy for the first appearance of sex will be the first stratigraphic occurrence of complex multicellularity.

Bangiomorpha pubescens is the first occurrence of complex multicellularity in the fossil record. A differentiated basal holdfast structure allowed for positive substrate attachment and thus the selective advantages of vertical orientation; i.e., an early example of ecological tiering. More generally, eukaryotic multicellularity is the innovation that established organismal morphology as a significant factor in the evolutionary process. As complex eukaryotes modified, and created entirely novel, environments, their inherent capacity for reciprocal morphological adaptation, gave rise to the “biological environment” of directional evolution and “progress.” The evolution of sex, as a proximal cause of complex multicellularity, may thus account for the Mesoproterozoic/Neoproterozoic radiation of eukaryotes.

Movements of the pelvic girdle have recently been found to contribute to inspiratory airflow in both crocodilians and birds. Although the mechanisms are quite different in birds and crocodilians, participation of the pelvic girdle in the production of inspiration is rare among vertebrates. This raises the possibility that the pelvic musculoskeletal system may have played a role in the ventilation of basal archosaurs. Judging from the mechanism of pelvic aspiration in crocodilians and the structure of gastralia in basal archosaurs, we suggest that an ischiotruncus muscle pulled the medial aspect of the gastralia caudally, and thereby helped to produce inspiration by increasing the volume of the abdominal cavity. From this basal mechanism, several archosaur lineages appear to have evolved specialized gastralia, pelvic kinesis, and/or pelvic mobility. Kinetic pubes appear to have evolved independently in at least two clades of Crocodylomorpha. This convergence suggests that a diaphragmatic muscle may be basal for Crocodylomorpha. The pelvis of pterosaurs was long, open ventrally, and had prepubic elements that resembled the pubic bones of Recent crocodilians. These characters suggest convergence on the pelvic aspiratory systems of both birds and crocodilians. The derived configuration of the pubis, ischium and gastralia of non-avian theropods appears to have enhanced the basal gastral breathing mechanism. Changes in structure of the pelvic musculoskeletal system that were present in both dromaeosaurs and basal birds may have set the stage for a gradual reduction in the importance of gastral breathing and for the evolution of the pelvic aspiration system of Recent birds. Lastly, the structure of the pelvis of some ornithischians appears to have been permissive of pubic and ischial kinesis. Large platelike prepubic processes evolved three times in Ornithischia. These plates are suggested to have been instrumental in an active expansion of the lateral abdominal wall to produce inspiratory flow. Thus, many of the unique features found in the pelvic girdles of various archosaur groups may be related to the function of lung ventilation rather than to locomotion.

Contrary to the geological stereotype of pure-carbonate reef platforms, approximately 50% of shallow shelf area in the Tropics is accumulating siliciclastic and mixed siliciclastic-carbonate sediments. Taphonomic characterization of these settings is thus essential for assessing variation among major facies types within the Tropics, as well as for eventual comparison with higher-latitude settings. Our grab samples and dredge samples of bivalve death assemblages from nine stations in five subtidal habitats in a large marine embayment of Caribbean Panama (Bocas del Toro) provide the first actualistic information on the taphonomic condition of shells in Recent tropical siliciclastic sediments. Focusing on unambiguous damage to bivalve shell interiors, we found that the quality of shell preservation in fine-grained siliciclastics is superb: commonly «10% of specimens are affected by encrustation, boring, edge-rounding fine-scale surface alteration via dissolution, microbioerosion maceration. Pure-carbonate and mixed siliciclastic-carbonate environments containing hard substrata (patch reefs, Halimeda gravelly sand, mud among patch reefs) contain higher numbers of more severely damaged shells (generally >25%) and also higher diversities of fossilizable encrusters and borers. Disarticulation and fragmentation are pervasive across all environments and are probably related to predation rather than to postmortem processes. As in other shallow subtidal study areas, the taxonomic compositions of death assemblages have not been homogenized by postmortem transport but show high spatial fidelity to the distribution of living species. Assemblages from the five sedimentary environments have distinct taphonomic signatures, but the strongest differences are between the two fine-grained, exclusively soft-sediment siliciclastic environments on the one hand and the three environments containing hard substrata on the other. Experimental tests for rates and agents of damage, still in progress, indicate that the most critical environmental variables are exhumation cycles and burial rate. Bivalve death assemblages from Bocas del Toro demonstrate that damage levels in tropical fine-grained siliciclastic environments are much lower than in closely associated reefs and algal sands suggest a less filtered record of biological information.

Taphonomy plays diverse roles in paleobiology. These include assessing sample quality relevant to ecologic, biogeographic, and evolutionary questions, diagnosing the roles of various taphonomic agents, processes and circumstances in generating the sedimentary and fossil records, and reconstructing the dynamics of organic recycling over time as a part of Earth history. Major advances over the past 15 years have occurred in understanding (1) the controls on preservation, especially the ecology and biogeochemistry of soft-tissue preservation, and the dominance of biological versus physical agents in the destruction of remains from all major taxonomic groups (plants, invertebrates, vertebrates); (2) scales of spatial and temporal resolution, particularly the relatively minor role of out-of-habitat transport contrasted with the major effects of time-averaging; (3) quantitative compositional fidelity; that is, the degree to which different types of assemblages reflect the species composition and abundance of source faunas and floras; and (4) large-scale variations through time in preservational regimes (megabiases), caused by the evolution of new bodyplans and behavioral capabilities, and by broad-scale changes in climate, tectonics, and geochemistry of Earth surface systems. Paleobiological questions regarding major trends in biodiversity, major extinctions and recoveries, timing of cladogenesis and rates of evolution, and the role of environmental forcing in evolution all entail issues appropriate for taphonomic analysis, and a wide range of strategies are being developed to minimize the impact of sample incompleteness and bias. These include taphonomically robust metrics of paleontologic patterns, gap analysis, equalizing samples via rarefaction, inferences about preservation probability, isotaphonomic comparisons, taphonomic control taxa, and modeling of artificial fossil assemblages based on modern analogues. All of this work is yielding a more quantitative assessment of both the positive and negative aspects of paleobiological samples. Comparisons and syntheses of patterns across major groups and over a wider range of temporal and spatial scales present a challenging and exciting agenda for taphonomy in the coming decades.

Statistical inference about mass extinction events is commonly based on the pattern of fossil finds among a group of taxa. An important issue for existing methods is the selection of taxa for inclusion in the analysis. A common approach is to select taxa on the basis of the stratigraphic height of their uppermost finds. This approach creates a bias in favor of detecting a mass extinction event. This paper describes and illustrates an approach that avoids this problem.

New morphometric data gathered from cross-sections of two Lower Devonian land plants (Rhynia gwynne-vaughanii and Asteroxylon mackiei) are interpreted in terms of the evolution of the function of vascular bundles in early land plants. The following conclusions can be drawn from these new data: (1) The ratio of the cross-sectional area of the xylem (representing the conducting volume supplying the axis with water) to the xylem perimeter (representing the “contact area” between xylem and parenchyma through which water leaves the xylem and enters the parenchyma) is not constant for Rhynia axes, almost constant for Asteroxylon axes, and different between Rhynia and Asteroxylon. Thus, Bowers hypothesis that the ratio of cross-sectional area of the xylem to xylem perimeter is constant during ontogenetic development is true for Asteroxylon. That this ratio is constant during phylogeny, however, is not supported by our data. (2) The ratio between cross-sectional area of xylem to parenchyma is higher in Asteroxylon than in Rhynia. (3) As predicted by previous computer simulations, the ratio of the xylem perimeter to the axis perimeter plays a major role in determining water transport performance of the transpiring axis. This ratio is constant within ontogeny but is different in Asteroxylon and Rhynia. In Asteroxylon axes, this ratio is about twice as large as in Rhynia axes. (4) Contrary to the expectations, the distance between the outermost layer of the xylem and the transpiring surface, which represents the low-conductivity pathway through the parenchyma, appears not to be a limiting factor for the water transport in axes of Rhynia and Asteroxylon. (5) From the analysis of the geometric parameters, it is evident that Rhynia and Asteroxylon with their distinct stelar geometries represent two different constructional types for which no transitional stages are known.

Phylogenetic analysis of the metazoan evolutionary tree as a whole, and of trees of component major clades, indicates that marine herbivores, defined here as macrophagous consumers of living multicellular attached marine plants, always occupy terminal positions at several scales of analysis. Nearly all living benthic marine herbivores are derived from microphages, detritivores, or predators, and most have post-Paleozoic origins. The derived nature of herbivory in the sea parallels the evolutionary situation among land animals. Pre-Mesozoic marine benthic ecosystems, characterized by relatively low rates of flow of energy and nutrients, may have relied even more heavily on decomposers for the transfer of carbon from primary producers to animals than do living marine ecosystems in the photic zone.

As paleobiology continues to address an ever broader array of questions, it becomes increasingly important to interpret confidently the meaning of the pattern of fossil occurrences as found in outcrop. To this end, sequence stratigraphy is an important tool for paleobiologists because it predicts the distribution of unconformities, facies changes, and changes in sedimentation rate, all factors known from numerous previous studies to affect the quality of the fossil record. Computer simulations now make it possible not only to model sequence architecture within sedimentary basins, but also to model the occurrence of fossils within those basins. These models generate predictions regarding the stratigraphic distribution of first and last occurrences, changes in species abundance, changes in species morphology, and the distribution of gaps in fossil ranges. Although confirmation of some of these predictions has been found in field studies, the extent to which these predictions describe the fossil record in general is still unknown. If the predicted patterns of fossil occurrences are found to be widespread, it will suggest that a relatively simple model of fossil occurrences in outcrops could become a new tool for solving a wide array of paleobiologic and biostratigraphic problems. With such models, paleobiologists and biostratigraphers will be able to use model data to test the accuracy of newly developed methods of analysis.

Data from a comprehensive literature survey for the first time provide stage-level resolution of Early Cretaceous through Pleistocene species diversity for nongeniculate coralline algae. Distributions of a total of 655 species in 23 genera were compiled from 222 publications. These represent three family-subfamily groupings each with distinctive present-day distributions: (1) Sporolithaceae, low latitude, mainly deep water; (2) Melobesioid corallinaceans, high latitude, shallow water, to low latitude, deep water; (3) Lithophylloid/mastophoroid corallinaceans, mid- to low latitude, shallow water.

Raw data show overall Early Cretaceous-early Miocene increase to 245 species in the Aquitanian, followed by collapse to only 43 species in the late Pliocene. Rarefaction analysis confirms the pattern of increase but suggests that scarcity of publications exaggerates Neogene decline, which was actually relatively slight.

Throughout the history of coralline species, species richness broadly correlates with published global paleotemperatures based on benthic foraminifer δ18O values. The warm-water Sporolithaceae were most species-abundant during the Cretaceous, but they declined and were rapidly overtaken by the Corallinaceae as Cenozoic temperatures declined.

Trends within the Corallinaceae during the Cenozoic appear to reflect environmental change and disturbance. Cool- and deep-water melobesioids rapidly expanded during the latest Cretaceous and Paleocene. Warmer-water lithophylloid/mastophoroid species increased slowly during the same period but more quickly in the early Oligocene, possibly reflecting habitat partitioning as climatic belts differentiated and scleractinian reef development expanded near the Eocene/Oligocene boundary. Melobesioids abruptly declined in the late Pliocene-Pleistocene, while lithophylloid/mastophoroids increased again. Possibly, onset of glaciation in the Northern Hemisphere (~2.4 Ma) sustained or accentuated latitudinal differentiation and global climatic deterioration, disrupting high-latitude melobesioid habitats. Simultaneously, this could have caused moderate environmental disturbance in mid- to low-latitude ecosystems, promoting diversification of lithophylloids/mastophoroids through the “fission effect.”

Extinction events that eliminated >20% of coralline species were most severe (58–67% of species) during the Late Cretaceous and late Miocene-Pliocene. Each extinction was followed by substantial episodes of origination, particularly in the Danian and Pleistocene.

Bivalve death assemblages from subtidal environments within the tropical Bocas del Toro embayment of Caribbean Panama permit a test of the extent to which levels of damage are determined by the intrinsic nature of shell supply (proportion of epifaunal species, thick shells, calcitic shells, low-organic microstructures), as opposed to the extrinsic postmortem environment that shells experience. Only damage to interior surfaces of shells was used, to ensure that damage was unambiguously postmortem in origin. We find that facies-level differences in patterns of damage (the rank order importance of postmortem encrustation, boring, edge-rounding, fine-scale surface degradation) are overwhelmingly controlled by environmental conditions: in each environment, all subsets of the death assemblage present the same damage profile. The composition of shell supply affects only the intensity of the taphonomic signature (i.e., percentage of shells affected) only in environments containing hard substrata (patch reefs, Halimeda gravelly sand, mud among patch reefs). In these environments, epifauna, whether aragonitic or calcitic and whether thin or thick, exhibit significantly higher damage than co-occurring infauna, probably due to the initial period of seafloor exposure they typically experience after death. Thick shells (>0.5 mm), regardless of life habit or mineralogy, are damaged more frequently than thin shells, probably because of selective colonization by fouling organisms. Calcitic shells show no consistently greater frequency of damage than aragonitic shells high-organic microstructures yield mixed patterns. Taphofacies surveys in such depositional systems could thus be confidently based on any subset of the fauna, including diagenetically residual assemblages of calcitic shells and thick-shelled molds. Further tests are needed to determine whether the higher levels of damage observed on some subsets of shells are a consequence of greater time-averaging (thus lower temporal resolution), greater exposure time, preferential attack (potential bias in relative abundance), or some combination of these. Paleobiologically, however, the implication is that ecological subsets of bivalve assemblages are not isotaphonomic, either in tangible damage or in probable bias, within hard-substrate environments, although they may be within soft-sediment environments. In actualistic studies, targeting broad classes of taxa for comparison across environments maximizes our ability to extrapolate taphonomic guidelines into the fossil record, where life habits, skeletal types shallow subtidal habitats have dramatically different patterns of abundance and deployment.

Chad is a key region for understanding early hominid geographic expansion in relation to late Miocene and Pliocene environmental changes, owing to its location 2500 km west from the Rift Valley and to the occurrence of sites ranging in age from about 6 to 3 Ma, some of which yield fossil hominids. To reconstruct changes in herbivore paleodiet and therefore changes in the paleoenvironment, we measured the carbon and oxygen isotope composition of 80 tooth-enamel samples from three time horizons for nine families of Perissodactyla, Proboscidea, and Artiodactyla. The absence of significant alteration of in vivo isotopic signatures can be determined for carbon, thus allowing paleodietary and paleoenvironmental interpretations to be made.

While the results generally confirm previous dietary hypotheses, mostly based on relative crown height, there are some notable surprises. The main discrepancies are found among low-crowned proboscideans (e.g., Anancus) and high-crowned rhinocerotids (Ceratotherium). Both species were more opportunistic feeders than it is usually believed. This result confirms that ancient feeding ecology cannot always be inferred from dental morphology or extant relatives.

There is an increase in the average carbon isotope composition of tooth enamel from the oldest unit to the youngest, suggesting that the environment became richer in C4 plants with time. In turn, more C4 plants indicate an opening of the plant cover during this period. This increase in carbon isotope composition is also recorded within genera such as Nyanzachoerus, Ceratotherium, and Hexaprotodon, indicating a change from a C3-dominated to a C4-dominated diet over time. It appears that, unlike other middle Pliocene hominid sites in eastern and southern Africa, this part of Chad was characterized by very open conditions and that savanna-like grasslands were already dominant when hominids were present in the area.

The preservation of compounds of biological origin (nucleic acids, proteins, carbohydrates, lipids, and resistant biopolymers) in terrigenous fossils and the chemical and structural changes that they undergo during fossilization are discussed over three critical stratigraphic levels or “time slices.” The youngest of these is the archeological record (e.g., <10 k.y. B.P.), when organic matter from living organisms undergoes the preliminary stages of fossilization (certain classes of biomolecule are selectively preserved while others undergo rapid degradation). The second time slice is the Tertiary. Well-preserved fossils of this age retain diagenetically modified biomarkers and biopolymers for which a product-precursor relationship with the original biological materials can still be identified. The final time slice is the Carboniferous. Organic material of this age has generally undergone such extensive diagenetic degradation that only the most resistant biopolymers remain and these have undergone substantial modification. Trends through time in the taphonomy and utility of ancient biomolecules in terrigenous fossils affect their potential for studies that involve chemosystematic and environmental data.

Fossil floras are an important source of quantitative terrestrial paleoclimate data. Many paleoclimate estimates are based on relationships observed in modern vegetation between leaf morphology and climate, such as the increase in the percentage of entire-margined species with increasing temperature and the increase in leaf size with increasing precipitation. An important question is whether these observed relationships are universal or regional; for example, recent studies suggest that significant differences exist between floras from three domains: the Northern Hemisphere, New Zealand/Australia, and subalpine zones. Also, debate exists over which statistical models of modern data sets, univariate or multivariate, provide the most accurate estimates of paleoclimate. In this study, 12 foliage samples from living Bolivian forests are compared with data sets from different regions. Models based on data sets from North America and Japan, namely the Climate-Leaf Analysis Multivariate Program (CLAMP) data set of J. A. Wolfe, and from east Asia produce reasonably accurate estimates of temperature and precipitation, suggesting that the climate-leaf morphology relationships for Bolivian vegetation do not differ significantly from those for Northern Hemisphere vegetation. The mean leaf size for a given mean annual precipitation is smaller than for a data set from the Western Hemisphere and Africa, but this difference is most likely due to different sampling methods. As for estimating climate from fossil floras, these results, along with the analysis of four other regional data sets, imply that the most accurate climate estimates will be produced by the predictor data set with the most similar climate-leaf morphology relationships. Unfortunately, our present lack of understanding of why climate-morphology relationships vary between the North America/Japan, New Zealand/Australia, and subalpine domains makes it difficult to identify data sets similar to paleofloras. Until we learn more, it is probably best to compare fossil floras to predictor data sets from the same domain. The performance of the various statistical methods depends on the nature of the predictor data set. Multiple regression analysis tends to produce the most accurate estimates for small data sets with a narrow range of environmental variation that have similar relationships to the flora, and linear regression or canonical correspondence analysis for the larger and more varied CLAMP data set. If a similar predictor data set is not available, then nearest-neighbor analysis can still produce accurate paleoclimate estimates.

Paleobiologists frequently hypothesize that a taxon's duration (i.e., the true span from origination to extinction) exceeds its stratigraphic range (i.e., the span from first appearance to last appearance in the fossil record). One can test hypothesized duration by assessing the plausibility of the implicitly hypothesized gaps between origination and first appearance and / or between last appearance and extinction. Several tests assess the probability of not finding a taxon over some stratigraphic gap. Because the likelihood of a hypothesis given data reflects the probability of the data given that hypothesis, these probabilities also give the likelihood of a hypothesized duration. However, many probability / likelihood tests require simplifying assumptions about unknown sampling parameters such as the consistency of sampling over time, sampling intensities for unknown ancestors, and actual sampling intensities themselves.

This paper examines the effects of sampling parameters on probability / likelihood tests and presents methods for testing hypotheses about these unknowns while testing hypotheses about true durations. Two data sets are used here as examples. One analysis tests the origination times among Paleozoic gastropods implied by phylogenetic inferences. The other analysis tests the extinction times among Maastrichtian ammonites implied by different numbers of extinction events. In both cases, hypotheses positing many gaps in the fossil record become more likely after accommodating uncertainty about sampling. However, the increased likelihoods are insufficient to prevent these hypotheses from being rejected in favor of hypotheses positing fewer gaps. In both cases, the conclusions are identical to those derived by simple methods using simple models for unknown sampling parameters. Although numerous factors can exaggerate the implausibility of gaps, making these factors parts of testable hypotheses is possible. Thus, excessive assumptions about sampling parameters need not hinder empirical testing of hypothesized durations.

A geometric analysis of fenestrate bryozoan lophophore shape and arrangement is conducted by creating a theoretical morphospace of apertural positioning within the colonial meshwork. Working from the assumption that fenestrate bryozoans needed to form a continuous filtering surface with contact between adjacent lophophores, we show that within the morphospace three regions exist for optimum close-packing of lophophores with circular projections; all other close-packing configurations in the morphospace require the existence of noncircular lophophores.

Examination of the actual distribution of 251 fenestrate colonies within the morphospace reveals that the morphospace regions occupied by fenestellids and polyporids are displaced and have little overlap, but that they are very similar in size and shape that the colonies scale similarly. With increasing size, fenestrate meshworks expand laterally faster than the branches widen and the proximodistal spacing of the apertures increases, apparently because the larger zooids require disproportionately more room for their lophophores.

Two of the optimum close-packing regions of the morphospace are occupied by fenestrates. The positioning of the fenestellid region within the morphospace suggests that these biserial bryozoans followed a proximodistal-row placement of the lophophores that the lophophores were generally equitentacular, with circular projections. The positioning of the polyporid region within the morphospace suggests that these polyserial bryozoans followed a diagonal-row placement of the lophophores that the lophophores were heteromorphic, with medial lophophores on the branch being more equitentacular whereas the laterally placed lophophores were obliquely truncate. The third optimum close-packing region in the morphospace, corresponding to a hypothetical lateral-row placement of the lophophores within the colony, is unoccupied. We suggest that hypothetical fenestrate morphologies in the vacant region of morphospace have branches that would be too narrow to support normally shaped zooids that the lateral-row placement of the lophophores would have required the branches of the colony to have been perfectly aligned throughout growth.